The Stem Heat Balance (“SHB”) method of estimating sap flow within a plant stem has been well established as being an accurate methodology applicable to sap flow behavior in many species under a diversity of field conditions. For instance, Lascano, Baumhhardt, and Lipe reported that consistent results had been obtained for grapevines during a 2-day period with overall accuracy ranging +/−5%. See, Measurement of Water Flow in Grapevines using the Stem Heat Balance Method, Am. J. Enol. Vitic. Vol. 43: (2), 1992. As another example, Devitt, Berkowitz, Schulte, and Morris reported that consistent results had been obtained for woody ornamental tree species with overall accuracy being +/−10% during a 3-day period. See, Estimating Transpiration for Three Woody Ornamental Tree Species using Stem-flow Gauges and Lysimetry, HortScience, Vol. 28 (3), March 1993.
Additional illustrative examples of the applicability of SHB methodology are described by O. Bethenod, N. Katerji, R. Goujet, J. M. Bertolini, and G. Rana in Determination and Validation of Corn Crop Transpiration by Sap Flow Measurement under Field Conditions, published in Theor. Appl. Climatol. 67, 153±160 (2000); and by Escalona, L. Flexas, J. and Medrano, H., in Comparison of Heat Balance and Gas Exchange Methods to Measure Transpiration in Irrigated and Water Stressed Grapevines, published in Acta Hort. 526 ISHS (2000). Moreover, U.S. Pat. Nos. 5,337,604 and 5,269,183, each entitled “Apparatus for Measuring Sap Flow,” issued Aug. 16, 1994 and Dec. 14, 1993, respectively, to Cornelius H. M. Van Bavel and Michael G. Van Bavel, further elucidate the state of the art regarding sap flow measuring apparatus; both the '604 and '183 patents are fully incorporated herein by reference.
Referring to FIG. 10 which appears in each of the '604 and '183 patents, and is repeated herein for convenience as FIG. 11, the original formula for SHB sap flow rate is based on the following energy balance formula:SF=(Pin−Qv−Qr)/Cp*dT (grams/second)  (1)wherein sap flow (SF) is derived from an energy balance having the following components: heat input, Pin or Qi; radial heat loss, Qr; axial heat loss, Qv; specific heat, Cp; and temperature change, dT. Formula I will be hereinafter referred to as “the “original formula” for SHB sap flow rate; since the present invention incorporates an enhanced but simplified version of this formula, the simplified formula will be hereinafter referred to as an “improved formula” for SHB sap flow rate and will be abbreviated as “iSHB” for convenience. As will be appreciated by those skilled in the art, prevalent implementation of current sap flow sensor technology incorporates two pair of thermocouples equally spaced above and below a heating element, which is wrapped around the exterior of a selected plant stem. But, as is known to practitioners in the art, a deficiency of such implementation has been that neither heat gain nor heat loss from heat storage in the sensor's measurement section has been considered in this sap flow calculation.
Continuing with prevalent sap flow sensor implementation, a thermopile with multiple junctions has typically been wired circumferentially of the heater—in order to compute the radial heat loss, Qr, as a function of axial heat loss, Qv, convective heat loss, Qf, and heat input, Qi or Pin.Pin=Qr+Qv+Qf (watts)  (2)The convective heat loss by the sap flow (Qf) is determined by rearranging equation 2, per the following equation:Qf=Pin−Qr−Qv (watts)  (3)
As will be appreciated by those skilled in the sap flow art, a heater strip provides energy into the stem (Pin) that may be readily computed from Ohm's law, i.e., Pin=V2/R, in which heater impedance, R in Ohms, corresponds to a measured and recorded constant, with voltage, V, being monitored at the sensor input or the heater voltage regulator output.
It will be understood that Qr, the radial heat loss, reaches a maximum at night, since there is usually minimal or no sap flow at night. Thermopile voltage, Ch in mV, may be measured for a few hours before dawn, and a zero set may be typically performed to determine the corresponding heat conductance constant, Ksh in w/mV, which may be computed from the energy balance assuming that convective heat loss, Qf, by the sap flow, is zero.Ksh=(Pin−Qv)/Ch (Watts/milliVolts)  (4)Once the constant Ksh has been determined, then radial heat loss, Qr, may be calculated. Experience teaches that the radial heat loss, Qr, decreases as more of the heat is absorbed by sap flowing through the stem:Qr=Ksh*Ch (Watts)  (5)
It will be understood by practitioners in the art that Fourier's Law describes the vertical, axial conduction along the upward path of heat flow, which may be subdivided into an upward component, Qu, and a downward component, Qd:Qv=Qu+Qd  (6)where Qu=Kst*A*dTu/dX and Qd=Kst*A*dTd/dX. Kst corresponds to thermal conductivity of the stem (Watts/meter-° K) established by previous testing for a variety of woody or herbaceous plants; A corresponds to the stem cross-sectional area (square meters) measured from each individual plant's diameter; dTu and dTd correspond to the upward and downward temperature gradients (° K) along the path of heat flow, respectively; and dX is the spacing between thermocouple junctions (meters).
It will be understood by those skilled in the art that, in U.S. Pat. No. 5,337,604, there are two differentially wired thermocouples—with each thermocouple measuring not only rising sap temperature, but also measuring axial heat conduction, Qv. Channel Ah measured the temperature difference A-Ha (mV); Channel Bh measured temperature differential B-Hb (mV). Subtraction of these two signals Bh-Ah yielded two signals proportional to axial heat conduction emanating out of stem section, Qu and Qd. Since the distances separating the upper thermocouple, TC, pair and lower TC pair were fixed by design to the same value for each particular sensor, the components of Qv were combined with common denominator, dX. The voltage measured by the thermocouple signals was then converted by a constant for a typical T-type thermocouple (0.040 mV/° C.) to temperature measured in ° C.Qv=Kst*A(BH−AH)/dX*0.040 mV/° C. (W)  (7)The temperature increase of the sap was measured by the same pair of thermocouples, by adding signals Ah and Bh, averaging, and then converting the resultant signal to ° C.:dT=(Ah+Bh)/2*0.040 (° C.)  (8)Computing convective heat loss, Qf, is then determined from equations (3), (5), and (7), whereupon Qf is then converted to sap flow. It will be understood that, to convert convective heat absorbed by the sap, Qf is divided by the specific heat of water (4.186 j/g ° C.), whereupon sap temperature increase may be obtained from equation (8).SF=(Qf)/Cp*dT (g/s)  (9)
Plant stem temperature variation known to be attributable to changes manifest between the ground and the stem—as a function of ambient fluctuations—is commonly defined as the “Natural Temperature Gradient” typically represented by acronym “NTG.” Test methods to determine NTG are invoked by practitioners in the art to confirm that a valid sap flow sensor installation has been achieved, and, occasionally, to adjust sensors in situ in the field as appropriate for refining sap flow calculations. See, for example, “The Effect of Environmentally Induced Stem Temperature Gradients on Transpiration Estimates from the Heat Balance Method in Two Tropical Woody Species,” by V. M. Gutierrez, A. R. Harrington, C. F. Meinzer, and H. J. Fownes published in Tree Physiol, 14:179-190, 1994).
As is well known in the art, NTG is most severe not only during the first two to four hours after sunrise, but also during periods of rainfall. At very low flow rates and on large stems, e.g., tree trunks having diameter greater than 50 mm, improvements to the SHB method have been suggested which account for heat storage, Qs. See, for example, “Including the Heat Storage Term in Sap Flow Measurements with the Stem Heat Balance Method” by V. L. Grime, J. I. L. Morison, and L. P. Simmonds, published in Agricultural and Forest Meteorology 74, 1-25, 1995. In other published examples based upon data obtained from a wide range of sensors, the heat storage effect has been found to be very small and thus cancels-out on a daily basis, under stable conditions.
If sap flux heat, Qf, were relatively small compared to large ambient stem heat variation, or if intense scrutiny of momentary or hour-by-hour sap flow were required, then more complex sensor construction and installation methods would be prerequisite to properly account for stored heat, Qs. Unfortunately, there have been no commercial products developed in the art that have engendered economic construction and/or an economic recording methodology. Moreover, there appears to have been no actual demand heretofore for such commercial Qs-measurement solutions. It will be understood by practitioners conversant in the art that the most severe effect of Qs is in the morning—just after sunrise—when heat stored in a sap flow sensor section is released via initial sap movement, followed by instantaneous upward heat dissipation into and through the ambient.
Problems with sap flow measurements under field conditions have been reported in published literature related to moisture and adventitious root development in plants such as corn, willow, and poplar trees. See, O. Bethenod, et al., “Determination and Validation of Corn Crop Transpiration by Sap Flow Measurement under Field Conditions” published in Theor. Appl. Climatol. 67, 153-160 (2000). Even in arid climates, characterized by inherently high evapotranspiration, plants transpire though their respective stems while moisture accumulation causes thermocouple damage over time. Practitioners in the art have learned that, to extend thermocouple lifespan to at least three years, sensors must be frequently moved to other locations—sometimes weekly, e.g., corn plants.
Moreover, unpublished reports emanating from the University of Arizona have described damage to sensors caused by moisture accumulation thereon, when such sensors have been installed on willow and poplar. In particular, it has been observed that moisture accumulation causes bark damage effectuated by mold and mildew, tending to cause consequential damage to sensor coatings and to implicated insulating collars. Eventually, corrosion causes damage to crucial sensing thermocouples and associated thermopile electronics. Since such corrosion damage is obviously irreparable, costly replacement of entire sap flow sensors would be required to sustain accurate field measurements of sap flow. For instance, in field applications of sap flow sensors on commercial grapevines, sensors typically remain in situ for several months. Accordingly, commercial services providing sap flow data have heretofore required costly recurring maintenance of sap flow sensors in the field.
It will be readily appreciated that field research projects and commercial applications usually require fitting sensors to a plethora of highly irregular shapes, especially manifest in environments featuring cultivated. Under such grape vine laden circumstances, vine trunks inherently twist and include tightly-spaced scars derived from old petioles, and frequent pruning. Furthermore, oval irregularly-shaped and scarred surfaces are manifest by cordons. Practitioners in the art have been challenged by a long-standing deficiency that sap flow apparatus seeking to commercially measure sap flow in corn, soybean, cotton, tomato, and many other crops lack a convenient and expeditious installation methodology that is not only inherently flexible and adaptable, but also affords significantly less-frequent maintenance and routinely effectively seals electronic wiring.
For commercial sap flow measurement applications on grapes and like crops, there is, of course, considerable variation of soil type, terrain, and irrigation-water distribution. While SHB sap flow methodology has been shown to be very effective, nevertheless, multiple plants in a particular field need to be monitored in order to generate measurements that are representative of variable field-water conditions. Indeed, experience has demonstrated that preferably at least four to eight plants should be monitored to obtain adequate statistics pertaining to water consumption and water stress.
In view of the substantial number of sensors required to adequately encompass a field of crops, from a practical vantage point, costs attributable to sensors and to data collection must be significantly reduced in order to gain wide commercial acceptance. As is well known to practitioners skilled in the art, a substantial portion of sensor construction cost has been attributable to labor associated with assembling prerequisite electronics. But, another substantial portion of sap flow measurement cost is attributable to construction of a reliable integrated sensor collar that includes and encompasses the contemplated number of electrical connections prerequisite for computing the energy balance from which sap flow may be converted.
It will be appreciated that current sap flow sensors implementing SHB methodology require four data signals for operation: two signals provided by each of two pair of differential thermocouples. In a manner known in the art, each differential thermocouple pair provides a signal not only indicative of temperature gradient above and below the sensor heater, respectively, but also indicative of conducted stem heat transfer. A third signal is generated from a thermopile, indicative of radial heat flux corresponding to heat loss to the ambient. A fourth signal is indicative of the millivoltage delivered to the sensor heater.
Signal processing data loggers, e.g., the “Flow4” System disclosed in U.S. Pat. No. 7,280,892, incorporated herein fully by reference, have proven to be relatively expensive due to the necessity for four differential channels required for each sensor connection. It will be appreciated by those skilled in the art that three of these four channels must be capable of resolving signals accurately to one microvolt. This demanding requirement and other factors render such monitoring apparatus rather expensive, thereby foreclosing many commercial applications which would clearly benefit from implementations of such Flow4 technology.
SHB sap flow sensor performance has been examined and analyzed during numerous scientific studies. Several publications elucidate computer simulations and report both expected accuracy and deviations manifest under strong ambient temperature changes at low flow rates. For example, Peramaki, Vesala and Nikinmaa, in 2001, published a study of the applicability of the heat balance method for estimating sap flow in boreal forest conditions. See, Boreal Env, Res 6:29-43 (ISSN 1239-6095).
Underestimates in steady-state conditions were reported to be caused by inaccurate sap temperature estimates. When early morning conditions were studied, NTG manifest as differences in air and sap temperatures, and the release of stored heat, Qs, causing problematic sap flow results having substantial peaks. For these early morning conditions, the problematic results suggested that measurements should be taken that were more representative of sap dT entering into the stem sensor, wherein the difference in rising sap temperature would devolve to significant accuracy-improvement. Contemporary experiential studies seem to demonstrate that dT sap temperature measurement is a critical prerequisite to achieving more accurate sap flow results.
Since the original SHB design has measured conduction equidistant above and below the sensor heater—manifest as equal amounts of Qu and Qd—typically dT will be zero or very close to zero at a zero sap flux state, Qf, every morning before dawn. Moreover, since dividing by zero or by nearly-zero causes infinite results, i.e., huge inaccuracies, software-based filters have been commonly used to disregard dT at low flow below 75° C., and to avoid division by zero. See, Dynamax Dynagage Manual and U.S. Pat. No. 7,280,892, col 10.
Sap flow simulations reported by Peramaki, Vesala and Nikinmaa, in view of studies of sensor construction have accommodated dT temperature sensors being positioned symmetrically, one pair slightly below the sensor heater and one pair slightly thereabove. Published research and computer simulations apparently have nevertheless not accommodated installations that typically require overlap of the sensor heater, which, in turn, inevitably causes an uneven distribution of heat across the plant's stem. Ergo, more heat is commonly concentrated at the heater strip overlap than otherwise, whereupon the dT (temperature) measurement is conventionally taken on the opposite side of the stem. Practitioners in the art will readily understand that this prevalent protocol causes a gradient that is manifest as a dT temperature underestimate, not contemplated by the simulations. It will be appreciated that this heater overlap is practicably unavoidable, so that a range of sensor diameters can be accommodated using a single sensor and a fixed heater width.
The sap flow means and techniques heretofore known by those skilled in the art have suffered from a panoply of deficiencies: failing to remove or diminish the effects of NTG; manifesting concerns for moisture damage to both plant and sensor; unreliably installing and implementing sensors over irregular plant surfaces; and requiring at least four data channels. This panoply of deficiencies has continued to render current sap flow detection and measurement technology unaffordable in many beneficial scenarios. Accordingly, these limitations and disadvantages of the prior art are overcome with the present invention, wherein improved means and techniques are provided which are especially useful for ascertaining sap flow in herbaceous plants and trees.